Contrary to a widespread opinion, the model of Hot Big Bang, far from profiting from irrefutable arguments of its solidity suffer from many and serious difficulties which we enumerated in chapter 3 (I Hot Big Bang - Conclusions).

The major arguments of the temporalist model which we propose can be summarized in three groups:

1) The existence of the temporalist quantum constant To and his consequences:

d) the constant of fine structure & = e² / hc = 1 / 137,036 = e / c x To

e) the redshift of the galaxies z = T / To (T being duration of course of radiation)

g) the quantum origin of the gravitation with the value of the intensity of the field of acceleration according to G' x To = c

The intervention of the temporalist constant To in these various phenomena, dependent or independent, cannot be put on the account of coincidences. The probability theory would cancel it. The existence of constant To seems impossible to circumvent. Only the temporalist model proposes a coherent interpretation of all these phenomena where the factor To appears. If the temporalist interpretation is rejected, the facts remain and one must propose a credible alternative. It does not seem possible for us to consider another one validly, currently.

2) In 1929, estimated by Hubble at 500 Km/sec/Mpc, the "pseudo-velocity of recession" of the galaxies converges today (after decades and more than 153.000 observations of redshifts by NASA) towards the value of 67,71 Km/sec/Mpc established theoretically in 1962 by the author. This theoretical value was obtained by purely physical considerations, independently of all given astronomical data, wich consolidates its validity.

3) The temporalist model implies and proposes a modification of the gravitation. The temporalist model of gravitation proposes an explanation detailed and coherent of dimensions of the structures of the universe, from the field of terrestrial gravitation to the greatest structures of several hundreds of megaparsecs (as well as comparable voids of dimensions). The model of Hot Big Bang notes these structures but is impotent to give an account of it.

The numerous theoretical difficulties of the model of Hot Big Bang which we quote at the beginning of this chapter disappear in the temporalist model. Let us quote and answer to them briefly:

Why does the expansion start beyond the Local Group? - The redshift and the escape effect start as of the emission of the photons.

The value of the constant of Hubble, corresponding to the age of the universe, in the model of Hot Big Bang, is a quantum and nonmacroscopic constant in the temporalist model. Its value, given theoretically in 1962, is 4,5546 10.17 sec., that is to say approximately 14,43 billion years. One must note that the most remote known quasar is located at 14,4 billion light-years (R. Becker and all. Astron.J. ready for press 2001).The relation of Hubble v = Hd changes, in the temporalist model into v = 1/To x T (with v effect of escape, To temporalist constant and T duration of propagation of the radiation) from where To = cT / v and in numerical values To = 2,997925 10.10 cm x 1,0287 10.14 sec (duration of 1 Mpc) / 6,771 10.6 cm = 4,5546 10.17 sec.

The universe cannot be homogeneous and isotropic on all the scales because of the rays of gravitation, different according to masses.

In the temporalist model, there are no expansion, no primordial explosion, no emergence of space, time and energy. There is no inflation. There is no cosmological constant. The cosmic microwave background radiation does not originate in Hot Big Bang. There is no primordial nucleosynthesis. There is no limit at the macroscopic age of the universe. There is no critical density of the universe. The structures of the universe on a large scale, just as the presence of great voids are the result of the existence of the gravitation with finished range and the rays of gravitation. The age of the galaxies clusters and old stars do not pose a problem in the temporalist model.

As we can see it, the major part of the difficulties of the model of Hot Big Bang, caused by this model of universe, disappear with the temporalist model. Only two possible difficulties can be retained in the temporalist model: the existence of the cosmic microwave background radiation and the current abundance of the light elements in the universe.

Cosmic microwave background radiation, as we indicated in chapter 2 ( d - Cosmic Microwave Background Radiation) is not a consequence of the sole model of Hot Big Bang. Its prediction had been made, without the use of the model of Hot Big Bang, and before Gamow by: Guillaume (1896), Eddington (1926), Regener (1933), Nernst (1933), McKellar and Herzberg (1941), Finlay-Freundlich (1953) and Max Born (1953). These authors had predicted temperatures going from 1,9 to 6 K (Andre Koch Torre Assis and Marcos Cesar Danhoni Neves - 1995). Moreover, the forecast, in 1953, by Gamow, of a cosmic radiation background at a temperature of 7 Kelvin degrees, was founded on a fallacious mathematical argument (Weinberg 1980). It is thus advisable to work out a model of the coherent cosmic microwave background radiation with the new data of the temporalist model.

It is the same for the current abundance of the light elements in the universe.

It is necessary to underline a significant element which changes everything in the analysis of these two phenomena, the existence of a macroscopic unbounded time and its consequences.

The temporalist model results from a simple postulate, that of the asymmetry of time and its application to the physics of the photon. From there rise, without other assumption, the existence of the temporalist quantum constant t and his quantum consequences (electric charge, photoelectric effect, constant of fine structure, etc...), the redshifts, the quantum constant of gravitation G', the temporalist gravitation and his model of formation of the structures of the universe.

THE EXPERIMENTAL FACT: the redshift z of the remote galaxies

Hot Big Bang :

The hypothesis of the Doppler effect

The hypothesis of the asymmetry of the time and the influence of the temporalist constant To on the propagation of the photon

Hot Big Bang :

Recession of the galaxies

Stationary universe

NEW HYPOTHESES :

Hot Big Bang :

1) expansion of the universe

2) explosion (Hot Big Bang) starting from a singularity of the space-time with an infinite density and temperature

3) inflation with a space expansion about 10^50

4) origin of space, time and energy

5) critical density of the universe

6) cosmological constant

7) origin of the CMBR

8) primordial nucleosynthesis  

1) stationary universe

2) no explosion and no singularity with infinite physical values

3) no inflation

4) the universe exists. It did not have a beginning and will not have any end

5) the universe does not have criticical density

6) it is no cosmological constant

7) the CMBR envisaged by Gamow was founded on a fallacious mathematical argument. Its existence had been envisaged, long before him, by many researchers

8) it is no primordial nucleosynthesis

Hot Big Bang :

1) the empirical estimate of the value of Ho, after several decades of improvements and more than 153.000 observations of redshifts of NASA (data bases IPAC - 2001) approaches the value of 70 Km/sec/Mpc

1) the temporalist model established, theoretically, since 1962, the value of Ho = 1/4,5546 10^17 sec and that of the escape effect of the galaxies: 67,71 Km/sec/Mpc

Hot Big Bang :

2) the problem of the horizon is solved only by the hypothesis of inflation. This one, which does not rest on any experimental fact, with a considerable extrapolation of the laws of physics, has theoretical justification only that to answer, by an ad hoc hypothesis, highly speculative, with the difficulties of Hot Big Bang. One does not know the cause of inflation

2) the problem of the horizon of Hot Big Bang does not arise. There was no inflation. The temporalist horizon is consisted the stop of time of 4,5546 x 10^17 sec where the redshift becomes infinite

Hot Big Bang :

3) Why does the expansion start beyond the Milky Way?

3) the redshift or the escape effect begins as early as the emission of the photon

Hot Big Bang :

4) Which are the causes of the primordial explosion?

4) There is no primordial explosion

Hot Big Bang :

5) What was there before the primordial explosion? Which is the origin of space, time and energy?

5) the universe exists; it has neither origin nor end. In the same way for space, time and energy

Hot Big Bang :

6) the observations show that the universe is almost entirely flat. Why? Only the ad hoc and speculative hypothesis of inflation makes it possible to answer it

6) No need for structure is imposed for the universe

Hot Big Bang :

7) the hypothesis of the cosmological constant is necessary to the concept of expanding universe

7) the cosmological constant introduced by Einstein was, in a second time, completely challenged by him. It estimated that it was the most serious error of its life. Nothing justifies, today, experimentally, the existence of this constant

Hot Big Bang :

8) the critical density of the universe determines its evolution and its future

8) There is not critical density of the universe because of the finished range of the temporalist gravitation

Hot Big Bang :

9) the quasi-uniformity of the CMBR poses the problem of the horizon, only solved by the ad hoc and speculative hypothesis of inflation

9) numerous interpretations of the origin of the CMBR were proposed, long before Gamow, by many researchers, without need for resorting to the highly speculative model of inflation

10) the model of the primordial nucleosynthesis suffers from many difficulties (lithium, deuterium 2D - baryons density - cf chapter 2)

10) There are no problem of primordial nucleosynthesis since this one does not exist. A recent observation is in serious contradiction with the primordial nucleosynthesis (the quasar APM 08279+5255 old of 13,5 billion years contains 3 times more iron than the solar system old of approximately 5 billion years - XMM-Newton - G Hasinger and S. Komossa - July 2002)

11) the very weak fluctuations of the CMBR are impotent to account for the existence and the formation of the great structures of the universe (galaxies, clusters and superclusters, large walls, voids)

11) the great structures of the universe rise naturally, qualitatively and quantitatively, of the finished range of the temporalist gravitation

12) There is discordance between the calculated age of the universe in various independent ways (the expansion, the oldest white dwarfs, the chemical elements, the stars of the globular clusters - cf chapter 2)

12) the temporalist constant To (4,5546 x 10^17 sec) is a quantum constant and does not impose any constraint on the age of the macroscopic structures (stars, galaxies, clusters, etc...)

13) the model of Hot Big Bang and its prolongation, the inflationary hypothesis, violate without any experimental base, a certain number of physical principles: the principle of conservation of energy, the stop the speed of the light for the propagation of any physical phenomenon, etc...

13) It respects strictly all the physical principles: the principle of conservation of energy, the constancy the speed of the light in the void, etc... It rests on only one postulate, the asymmetry of time and its consequences: the influence of constant To on the propagation of the photon, the various quantum parameters, the finished range of the gravitation, etc...

14) to alleviate the many difficulties of the model, one adds hypotheses on hypotheses: inflation, chaotic inflation, auto-reproduction of universe, multiple universes, parallel universes, creations of universe in laboratory........ Nothing limits any more delirant imagination since any experimental bond with reality is broken!!

14) It endeavours to avoid any speculation which cannot be confirmed by the facts, in accordance with the principle of Popper. It thus proposes a certain number of tests likely to confirm it or to contradict it

Certain observational facts or tests seem likely to decide between the temporalist model and the model of Hot Big Bang.

1) According to the model of Hot Big Bang, the expansion starts beyond the Local Group of galaxies. According to the temporalist model, the redshift occurs as of the emission of the photon. Perhaps would it be possible, by a statistical analysis of speeds of stars, with border of our Local Group, to highlight the evidence the regular shift towards the red of radiation, according to the distance (or the duration), below the very limits of Local Group ?

2) Another observational test can, if it is realizable, slice in a decisive way between the universe spatially relatively static of the temporalist model and the expanding universe of Hot Big Bang. Indeed, if we compare the spectra of the galaxies with, for example, 50 years of interval, two cases of figure are possible. In the temporalist universe, the spectrum of the stationary remote galaxies, located at 13 - 14 billion light-years of us will not have varied. On the other hand, in an expanding universe, in 50 years, the galaxies expanding at relativistic speeds, being located from us further, will have a speed and thus a redshift different from those which they had 50 years earlier. If it were possible to highlight the difference or the absence in difference of the shift wavelengths of the spectrum of the remote galaxies, between two 50 years observations distant, this result would constitute a decisive test to slice between the temporalist model and the model of expansion of Hot Big Bang.

3) One can consider two series of tests of the temporalist model, the ones founded on space, the others on time. In the first category, the preceding test would make it possible to choose between a stationary temporalist universe and an expanding universe. Other tests are based on the coordinate of time. Thus, according to the temporalist model, a radiation being propagated in space undergoes a redshift. This shift due to the existence of the temporalist constant To does not depend on traversed space but on past time. One can thus consider a test allowing to detect this temporal or temporalist redshift of a radiation, according to past time. An experimentation as the Virgo project where a laser beam crosses an optical way of 150 km could allow, if required, to confirm or cancel the temporalist model. Other similar tests can be imagined. According to the temporalist model, a laser beam considered between two mirrors for a certain length of time undergoes a redshift. This shift, if one could detect it by rather precise measurements, could confirm or cancel the temporalist model.

4) In the field of the gravitation, the temporalist model proposes the finished range of the fields of gravitation, in opposition with the other theories of the gravitation. Chapter 10 (Masses and ray of gravitation) enumerates ten cases which confirm this proposal. One can plan, if the smallness of the effects were measurable, to check the finished range of the ray of gravitation in experiments comparable with that of the torsion bars of Etwöös.

The temporalist model, as we have seen, proposes considerable possible tests of its refutability, following Popper's meaning.

For more than 20 years a problem has intrigued the planetary scientists and physicists " a tiny, unexplained sunward acceleration in the motions of the Pioneer 10, Pioneer 11, and Ulysses spacecraft " (www.geocities. com/solarstormmonitor/Pioneer.html).Many other sites on the Web bring information on this subject.

This anomalous acceleration has several characteristics:

1) Its value, according to authors', would be of 7,59 x 10^-8 cm/sec^2 (http://renshaw.teleinc.com/papers/prl-pi/prl-pi.stm),

8,74 (+or - 1,33) x 10^-8 cm/sec^2 (http://csep10.phys.utk.edu/newsgroups/mond/messages/22.html),

" about 10 billion times smaller than the acceleration we feel from Earth' s gravitational pull " (www.geocities. com/solarstormmonitor/Pioneer.html - http://spaceprojects.arc.nasa.gov/Space_Projects/pioneer/PNStat.html).

2) The order of magnitude of this anomalous acceleration is c x Ho (Hubble constant).

3) This anomalous acceleration, independent of the distance, is constant for a spacecraft velocity.

4) This anomalous acceleration is radial.

This unexplained effect resulted very precisely from the universal temporalist isotropic field of acceleration G' = c / To with G' temporalist constant of gravitation, c speed of the light and To temporalist constant is 6,582 x 10^-8 cm/sec^2 = 2,997925 x 10^10 cm/sec / 4,5546 X 10^17 sec.

The temporalist model proposes:

1) The order of magnitude of this anomalous acceleration c x Ho (Hubble constant) corresponds to the temporalist model with c / To (Ho = 1/To) = G '.

2) When the spacecrafts leave a circular or elliptic trajectory to take a radial trajectory directed out of the solar system, the influence of the universal temporalist field of acceleration appears and slows down the speed of the spacecrafts (Pioneer 10, Pioneer 11, Ulysses, Galileo, etc...).

3) The universal temporalist field of acceleration does not disturb the circular or elliptic orbits of the planets of the solar system but only the radial trajectories.

4) An experimental measurement validates the temporalist model. In September 1998, the slowing of the speed of Pioneer 10 had led to a delay on its envisaged trajectory of approximately 400.000 km. The radial trajectory of Pioneer 10 started between 1973 and 1974 had thus lasted approximately 24,5 years is 7,73 x10^8 sec. The deceleration for this duration with a constant of acceleration of 6,582 x 10^-8 cm/sec^2 is equal to 6,582 x 10^-8 cm/sec^2 x 7,73 x 10^8 sec x 7,73 x 10^8 sec = 3,93293 x 10^10 cm = 393293 km.

5) Unlike to the traditional forecasts, all the spacecrafts and in particular Pioneer 10, which move away from the sun with a radial trajectory, will stop in galactic space when their speed is reduced to zero by the universal temporalist field of acceleration G ', if they are distant from other stars.

The temporalist model proposes that the mystery of the radial anomalous acceleration is solved, theoretically, by the temporalist model which it validates

The temporalist model rests on a fundamental and single postulate, the existence of the quantum constant To. It proposes a new approach of the physical universe. Its largest force of credibility, is according to us, to bring closer facts, apparently very distant, like the redshift from the galaxies, to the fundamental constants of the quantum electrodynamics and the gravitational phenomena. This synthesis was neither required nor wanted. It rises, in a natural way, from the existence of the temporalist constant To.

The temporalist model proposes a universe very different from the expanding universe of Hot Big Bang:

The universe does not know an expansion and is relatively stationary.

The universe knew neither primordial explosion, neither inflation phase, nor primordial nucleosynthesis, nor emergence of time, space and energy.

The universe does not have critical density.

The universe does not have a cosmological constant.

The universe exists. It did not have a beginning and will not have any end.

The temporalist constant To is a quantum and nonmacroscopic constant.

There are nevertheless a temporalist horizon, a stop, imposed by the existence of constant To and the redshift of radiations.

The universe does not have an age but macroscopic lifespans ago (of stars, galaxies, structures on a large scale, etc...) which can possibly exceed the value of constant To : 4,5546 x 10^17 sec.

The universe, spatially, does not have limits. The visible universe is limited by the temporalist horizon.

The gravitation has a finished range, proportional to the masses. The rays of gravitation determine dimensions and the distances from the structures of the universe (galaxies, clusters, voids, etc...).

The universe is relatively stationary in space but evolutionary in time.

The dark matter (or missing matter) is estimated from 90 to 99 % of the total matter. One detects it in the galaxies, the galaxies clusters, as well as in the greatest structures of the universe. Many candidates were proposed (MACHOs, neutrinos, WIMPs, brown dwarf stars, supermassif black holes, etc...) but, for the moment, its nature remains unknown.

Which are the currently well-known characters of the dark matter ?

1) the dark matter follows mainly the luminous matter in its localization in the galaxies, the galaxies clusters and even the great structures of a few ten of megaparsecs

2) the dark matter follows the irregularities of density of distribution of luminous matter in all the visible universe

3) the dark matter represents of 10 with 100 times the mass of luminous matter

4) the dark mass does not exist or is not perceptible in the large voids of several ten with several hundred of megaparsecs (Richard Schaeffer 2001)

We propose the identification of temporalist field of acceleration with dark matter.We indicate below the arguments in favour of our proposal:

1) the temporalist field emanating from the photons, therefore sources of light, well corresponds to the space distribution of the dark mass

2) the temporalist field, because of its origin, follows necessarily the irregularities of the density of distribution of luminous matter in all the visible universe

3) the temporalist field, according to the temporalist model, emanates from the damping of the vibrations of the photons and thus of a constant loss of energy (redshift). The fact that the percentage from 90 to 99 % of dark matter is located in the universe near the sources of light is in phase with the assumption of their temporalist origin

4) a contrario, the great voids which are not containing luminous matter cannot thus contain dark matter

5) the temporalist field is not a hypothetical field but a field which necessarily rises from the temporalist model

6) the temporalist field, whose vectors are gravitons, is not a luminous field

The temporalist model proposes a physical universe structured by three normative constants which constitute the borders of our world: h, c and To. The relations between these fundamental universal constants generate all the richness of the physical universe.